Am new to this, but have utilized the site often for protocol research.

Welcome

I am looking to remove RNase h from a sample and am unsure if electrophoresis will do the trick, or if there might be a better method.

for what purpose? If it is to just clean up DNA, a simple phenol-chloroform extraction or a DNA kit extraction will work fine.

I am not sure if simple de-naturation via high temp in a PCR would also help.

No - RNases are very good at re-folding post denaturation.

I am planning on utilizing native PAGE gel, probably 10% to start, with post run staining (Sybr AU) as our lab is not to keen on using EtBr.

That process should work, but you also need to think about how you will elute the DNA from the gel. It would also pay to have a close look at the % gels for DNA and maximal resolution. I don't think that DNA gels will be denaturing enough to stop RNases.